The advent of black-box deep neural network classification models has sparked the need to explain their decisions. However, in the case of generative AI such as large language models (LLMs), there is no class prediction to explain. Rather, one can ask why an LLM output a particular response to a given prompt. In this paper, we answer this question by proposing, to the best of our knowledge, the first contrastive explanation methods requiring simply black-box/query access. Our explanations suggest that an LLM outputs a reply to a given prompt because if the prompt was slightly modified, the LLM would have given a different response that is either less preferable or contradicts the original response. The key insight is that contrastive explanations simply require a distance function that has meaning to the user and not necessarily a real valued representation of a specific response (viz. class label). We offer two algorithms for finding contrastive explanations: i) A myopic algorithm, which although effective in creating contrasts, requires many model calls and ii) A budgeted algorithm, our main algorithmic contribution, which intelligently creates contrasts adhering to a query budget, necessary for longer contexts. We show the efficacy of these methods on diverse natural language tasks such as open-text generation, automated red teaming, and explaining conversational degradation.